Quantum walks, deformed relativity, and Hopf algebra symmetries

We show how the Weyl quantum walk derived from principles in Ref. [1], enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras--the usual Poincar\'e and the k-Poincar\'e algebras.